YES

Problem:
 div(X,e()) -> i(X)
 i(div(X,Y)) -> div(Y,X)
 div(div(X,Y),Z) -> div(Y,div(i(X),Z))

Proof:
 DP Processor:
  DPs:
   div#(X,e()) -> i#(X)
   i#(div(X,Y)) -> div#(Y,X)
   div#(div(X,Y),Z) -> i#(X)
   div#(div(X,Y),Z) -> div#(i(X),Z)
   div#(div(X,Y),Z) -> div#(Y,div(i(X),Z))
  TRS:
   div(X,e()) -> i(X)
   i(div(X,Y)) -> div(Y,X)
   div(div(X,Y),Z) -> div(Y,div(i(X),Z))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [i#](x0) = 4x0,
    
    [div#](x0, x1) = 4x0 + x1 + 7,
    
    [i](x0) = 3x0 + 1,
    
    [div](x0, x1) = 3x0 + x1 + 2,
    
    [e] = 2
   orientation:
    div#(X,e()) = 4X + 9 >= 4X = i#(X)
    
    i#(div(X,Y)) = 12X + 4Y + 8 >= X + 4Y + 7 = div#(Y,X)
    
    div#(div(X,Y),Z) = 12X + 4Y + Z + 15 >= 4X = i#(X)
    
    div#(div(X,Y),Z) = 12X + 4Y + Z + 15 >= 12X + Z + 11 = div#(i(X),Z)
    
    div#(div(X,Y),Z) = 12X + 4Y + Z + 15 >= 9X + 4Y + Z + 12 = div#(Y,div(i(X),Z))
    
    div(X,e()) = 3X + 4 >= 3X + 1 = i(X)
    
    i(div(X,Y)) = 9X + 3Y + 7 >= X + 3Y + 2 = div(Y,X)
    
    div(div(X,Y),Z) = 9X + 3Y + Z + 8 >= 9X + 3Y + Z + 7 = div(Y,div(i(X),Z))
   problem:
    DPs:
     
    TRS:
     div(X,e()) -> i(X)
     i(div(X,Y)) -> div(Y,X)
     div(div(X,Y),Z) -> div(Y,div(i(X),Z))
   Qed